Question

1. An overseas shipment of 5 foreign automobiles contains 2 that have slight paint blemishes. If an agency receives 3 of these automobiles at random, list the elements of the sample space S, using the letters B and N for blemished and nonblemished, respectively; then to each sample point assign a value x of the random variable X representing the number of automobiles with paint blemishes purchased by the agency.

Answer 1

The overseas shipment has 5 automobiles out of which 2 have slight paint blemishes.

Automobiles can be: $[A_1,A_2,A_3,B_1,B_2]$

where $A_i's$ denotes the non-blemished and $B_i's$ denotes the blemished ones.

Let X be the number of automobiles purchased with paint blemishes.

Element of sample space S for X $=0,1,2$

Case 1: For $X=0$

Sample space will be $(A_1,A_2,A_3)$

Case 2: For $X=1$

Sample space will be:

$[(A_1,A_2,B_1),(A_1,A_2,B_2),(A_1,A_3,B_1),\\ (A_1,A_3,B_2),(A_3,A_2,B_1),(A_3,A_2,B_2)]$

Case 3: For $X=2$

Sample space will be:

$[(A_1,B_1,B_2),(A_2,B_1,B_2),(A_3,B_1,B_2)]$